If you have the Race Lite Aero Clip-On Aerobar, that is the two separate bars.......yes you should be able to clip them on the underside of the handle bar, and fit the arm and hand rests back up the right way.

However it looks like you then would need extra padding on the arm rests to get your arms comfortably above the handle bar.

As far as I can tell the Race X lite Clip-on have the mounting bracket in one piece making it virtually impossible to fit to the underside of the handle bar.